The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A319518

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A319518

Number of sets of nonempty words with a total of n letters over n-ary alphabet such that if a letter occurs in the set all predecessors occur at least once.
(history; published version)

#17 by Alois P. Heinz at Thu Mar 10 09:31:26 EST 2022

STATUS

proposed

approved

#16 by Jean-François Alcover at Thu Mar 10 08:38:56 EST 2022

STATUS

editing

proposed

#15 by Jean-François Alcover at Thu Mar 10 08:38:51 EST 2022

MATHEMATICA

h[n_, i_, k_] := h[n, i, k] = If[n == 0, 1, If[i < 1, 0,

Sum[h[n - i*j, i - 1, k]*Binomial[k^i, j], {j, 0, n/i}]]];

a[n_] := Sum[Sum[(-1)^i*Binomial[k, i]*h[n, n, k-i], {i, 0, k}], {k, 0, n}];

Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Mar 10 2022, after Alois P. Heinz *)

STATUS

approved

editing

#14 by Alois P. Heinz at Sun Sep 23 14:03:37 EDT 2018

STATUS

editing

approved

#13 by Alois P. Heinz at Sun Sep 23 13:59:46 EDT 2018

CROSSREFS

Cf. A257741.

STATUS

approved

editing

#12 by Alois P. Heinz at Sun Sep 23 13:56:58 EDT 2018

STATUS

editing

approved

#11 by Alois P. Heinz at Sun Sep 23 13:56:28 EDT 2018

NAME

Number of sets of nonempty words with a total of n letters over n-ary alphabet such that if a letter occurs in the set all predecessors occur at least once.

#10 by Alois P. Heinz at Sun Sep 23 13:45:31 EDT 2018

MAPLE

h:= proc(n, i, k) option remember; `if`(n=0, 1, `if`(i<1, 0,

add(h(n-i*j, i-1, k)*binomial(k^i, j), j=0..n/i)))

end:

a:= n-> add(add((-1)^i*binomial(k, i)*h(n$2, k-i), i=0..k), k=0..n):

seq(a(n), n=0..20);

#9 by Alois P. Heinz at Sun Sep 23 10:54:24 EDT 2018

LINKS

Alois P. Heinz, <a href="/A319518/b319518.txt">Table of n, a(n) for n = 0..300</a>

#8 by Alois P. Heinz at Fri Sep 21 21:25:57 EDT 2018

EXAMPLE

a(0) = 1: {}.

a(21) = 41: {a}, {ab}, {ba}, {a,b}.

a(2) = 4: {aa}, {ab}, {ba}, {a,b}.